-6X(-4X+8)=9(-6X+3)

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Solution for -6X(-4X+8)=9(-6X+3) equation:


Simplifying
-6X(-4X + 8) = 9(-6X + 3)

Reorder the terms:
-6X(8 + -4X) = 9(-6X + 3)
(8 * -6X + -4X * -6X) = 9(-6X + 3)
(-48X + 24X2) = 9(-6X + 3)

Reorder the terms:
-48X + 24X2 = 9(3 + -6X)
-48X + 24X2 = (3 * 9 + -6X * 9)
-48X + 24X2 = (27 + -54X)

Solving
-48X + 24X2 = 27 + -54X

Solving for variable 'X'.

Reorder the terms:
-27 + -48X + 54X + 24X2 = 27 + -54X + -27 + 54X

Combine like terms: -48X + 54X = 6X
-27 + 6X + 24X2 = 27 + -54X + -27 + 54X

Reorder the terms:
-27 + 6X + 24X2 = 27 + -27 + -54X + 54X

Combine like terms: 27 + -27 = 0
-27 + 6X + 24X2 = 0 + -54X + 54X
-27 + 6X + 24X2 = -54X + 54X

Combine like terms: -54X + 54X = 0
-27 + 6X + 24X2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + 2X + 8X2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-9 + 2X + 8X2)' equal to zero and attempt to solve: Simplifying -9 + 2X + 8X2 = 0 Solving -9 + 2X + 8X2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + 0.25X + X2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 0.25X + 1.125 + X2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 0.25X + X2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 0.25X + X2 = 0 + 1.125 0.25X + X2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 0.25X + X2 = 1.125 The X term is 0.25X. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25X + 0.015625 + X2 = 1.125 + 0.015625 Reorder the terms: 0.015625 + 0.25X + X2 = 1.125 + 0.015625 Combine like terms: 1.125 + 0.015625 = 1.140625 0.015625 + 0.25X + X2 = 1.140625 Factor a perfect square on the left side: (X + 0.125)(X + 0.125) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (X + 0.125) equal to 1.068000468 and -1.068000468.

Subproblem 1

X + 0.125 = 1.068000468 Simplifying X + 0.125 = 1.068000468 Reorder the terms: 0.125 + X = 1.068000468 Solving 0.125 + X = 1.068000468 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + X = 1.068000468 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + X = 1.068000468 + -0.125 X = 1.068000468 + -0.125 Combine like terms: 1.068000468 + -0.125 = 0.943000468 X = 0.943000468 Simplifying X = 0.943000468

Subproblem 2

X + 0.125 = -1.068000468 Simplifying X + 0.125 = -1.068000468 Reorder the terms: 0.125 + X = -1.068000468 Solving 0.125 + X = -1.068000468 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + X = -1.068000468 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + X = -1.068000468 + -0.125 X = -1.068000468 + -0.125 Combine like terms: -1.068000468 + -0.125 = -1.193000468 X = -1.193000468 Simplifying X = -1.193000468

Solution

The solution to the problem is based on the solutions from the subproblems. X = {0.943000468, -1.193000468}

Solution

X = {0.943000468, -1.193000468}

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